The prize, with an award of about $81,000, was announced in London at the start of London Collections: Men, a round of fashion shows for menswear.
The street-inspired designers have had a rapid rise in the industry and recently added womenswear after taking the Council of Fashion Designers of America award in the men's category.
For the Woolmark Prize, founded by Australian sheep farmers in 1936, Public School was chosen by judges over four other brands: Sise of Japan, Asger Juel Larsen of Denmark, Strateas.Carlucci of Australia and The Emperor 1688 of United Arab Emirates.
"The great thing about Public School is the way in which they have mixed the traditional with the contemporary, creating an incredibly vibrant collection," Dylan Jones, editor of British GQ and a judge, said in a statement.
The duo's collection in Merino wool included boxy pieces in black and grey. One look paired loose short trousers with a slouchy short-sleeve cowl neck fitted with string ties.
"Many items were fully fashioned, so for sportswear they could fit the shape of the body and could work for some of the major sportswear brands," said another judge, menswear designer Paul Smith.
Osborne and Chow said in the statement they were "really proud" to have one. Their wool collection will be available in select retailers around the world starting in August.